Algorithmic ribbonness conjecture for alternating knots

An alternating knot is a knot admitting a diagram in which over- and under-crossings alternate as one travels along each component. A ribbon disk is a smoothly immersed disk in the four-ball whose singularities are ribbon singularities; a ribbon disk with three critical points has one minimum, one saddle, and one maximum in a Morse presentation. A knot is algorithmically ribbon if it is detected as ribbon by the algorithm described in the paper.

Algorithmic ribbonness conjecture. If an alternating knot admits a ribbon disk with three critical points, then it is algorithmically ribbon.

The conjecture asserts that the algorithm detects every such ribbon disk for alternating knots. The source gives experimental evidence and optimism for the claim, but no resolution is stated.